Asked by Rebekah Gonzalez on May 06, 2024

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A competitive market is made up of 100 identical firms. Each firm has a short-run marginal cost function as follows:
MC = 5 + 0.5Q,
where Q represents units of output per unit of time. The firm's average variable cost curve intersects the marginal cost at a vertical distance of 10 above the horizontal axis. Determine the market short-run supply curve. Calculate the price that would make 2,000 units forthcoming per time period. Note the minimum price at which any quantity would be placed on the market.

Marginal Cost Function

A mathematical representation that describes how the cost of producing one additional unit of a good varies as the quantity of production changes.

Market Short-Run Supply

The total quantity of a good or service that producers are willing and able to sell at current prices in the short run, considering fixed and variable costs.

Units of Output

The individual items or quantities produced by a process or system.

  • Comprehend the connection between marginal cost, average variable cost, fixed costs, and their consequences for short-run supply curves.
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ZK
Zybrea KnightMay 08, 2024
Final Answer :
The market supply curve is the horizontal summation of the individual firms' MC curves above the intersection with the respective average variable cost curves. We must express the quantity in terms of MC or:
Q = 2MC - 10.
Now add the 100 short-run supply curves together:
Q1 = 2MC - 10
Q2 = 2MC - 10
. . .
. . .
. . .
Q100 = 2MC - 10
__________________________ The market supply curve is the horizontal summation of the individual firms' MC curves above the intersection with the respective average variable cost curves. We must express the quantity in terms of MC or: Q = 2MC - 10. Now add the 100 short-run supply curves together: Q<sub>1</sub> = 2MC - 10 Q<sub>2</sub> = 2MC - 10 . . . . . . . . . Q<sub>100</sub> = 2MC - 10 <sup>______________</sup><sup>__________</sup><sup>__</sup><sup> </sup>   = 200MC - 1000 Now, solve for MC MC =   MC = 0.005ΣQ + 5 (above MC = 10) At ΣQ = 2000, the price would be P = MC = 0.005(2000) + 5 = $15 per unit. The lowest point on the supply curve would be just above the intersection with the average variable cost curve (at 10 units above the horizontal axis). = 200MC - 1000
Now, solve for MC
MC = The market supply curve is the horizontal summation of the individual firms' MC curves above the intersection with the respective average variable cost curves. We must express the quantity in terms of MC or: Q = 2MC - 10. Now add the 100 short-run supply curves together: Q<sub>1</sub> = 2MC - 10 Q<sub>2</sub> = 2MC - 10 . . . . . . . . . Q<sub>100</sub> = 2MC - 10 <sup>______________</sup><sup>__________</sup><sup>__</sup><sup> </sup>   = 200MC - 1000 Now, solve for MC MC =   MC = 0.005ΣQ + 5 (above MC = 10) At ΣQ = 2000, the price would be P = MC = 0.005(2000) + 5 = $15 per unit. The lowest point on the supply curve would be just above the intersection with the average variable cost curve (at 10 units above the horizontal axis). MC = 0.005ΣQ + 5 (above MC = 10)
At ΣQ = 2000, the price would be
P = MC = 0.005(2000) + 5 = $15 per unit.
The lowest point on the supply curve would be just above the intersection with the average variable cost curve (at 10 units above the horizontal axis).